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Summary form only given. We theoretically study the spin waves in an aperioci antiferromagnetic(AF)/ nonmagnetic(NM) multilayer, where the AF layer and the NM layer are arranged in the k-component Fibonacci sequence. The dispersion relation of magnetostatic spin waves and the precession amplitude of the total magnetization are obtained. The multiformity in frequency spectra leads to the tunable spin wave, which may benefit to make tunable devices of spin waves and achieve potential applications on microwave communications.